Pliant or compliant elements for harnessing the forces of moving fluid to transport fluid or generate electricity

ABSTRACT

Pliant, or compliant mechanisms for extracting electrical energy or useful work from a moving fluid are described. Persistent deformations in flexible elements are maintained with deformation retaining, or restraining components. The deformation retaining components may, in various embodiments, include rigid or tensile members, elastic coils, and/or the like. The deformations of the mechanisms may be configured so as to receive forces from moving fluid and transfer those forces in a variety of ways so as to pump fluid or generate electricity from this pumped fluid, or to generate electricity from material strains induced by moving fluid.

PRIORITY CLAIM AND RELATED APPLICATIONS

This application is a Non-Provisional of prior U.S. provisional patentapplication Ser. No. 61/227,279 entitled, “Compliant Elements,” filedJul. 21, 2009, to which priority under 35 U.S.C. §119 is claimed.

This application is also a Continuation-In-Part of and claims priorityunder 35 U.S.C. §120 to prior U.S. non-provisional patent applicationSer. No. 12/242,144 entitled, “PLIANT MECHANISMS FOR EXTRACTING POWERFROM MOVING FLUID,” filed Sep. 30, 2008 now U.S. Pat. No. 7,696,634,which in turn is a Continuation of and claims priority under 35 U.S.C.§120 to U.S. non-provisional patent application Ser. No. 12/150,910entitled, “Power generator for extracting power from fluid motion,”filed May 1, 2008, which in turn is a Non-Provisional of and claimspriority under 35 U.S.C. §119 to U.S. provisional patent applicationSer. No. 60/926,984 filed May 1, 2007.

This application is also a Continuation-In-Part of and claims priorityunder 35 U.S.C. §120 to prior U.S. non-provisional patent applicationSer. No. 12/569,762 entitled, “Pliant Mechanisms for Extracting Powerfrom Moving Fluid,” filed Sep. 29, 2009 now U.S. Pat. No. 7,839,007,which in turn is a Continuation of and claims priority under 35 U.S.C.§120 to prior U.S. non-provisional patent application Ser. No.12/242,144 entitled, “PLIANT MECHANISMS FOR EXTRACTING POWER FROM MOVINGFLUID,” filed Sep. 30, 2008, which in turn is a Continuation of andclaims priority under 35 U.S.C. §120 to U.S. non-provisional patentapplication Ser. No. 12/150,910 entitled, “Power generator forextracting power from fluid motion,” filed May 1, 2008, which in turn isa Non-Provisional of and claims priority under 35 U.S.C. §119 to U.S.provisional patent application Ser. No. 60/926,984 filed May 1, 2007.

This application is also a Continuation-In-Part of and claims priorityunder 35 U.S.C. §120 to prior U.S. non-provisional patent applicationSer. No. 12/575,434 entitled, “Pliant Mechanisms for Extracting Powerfrom Moving Fluid,” filed Oct. 7, 2009 now U.S. Pat. No. 7,863,768,which in turn is a Continuation of and claims priority under 35 U.S.C.§120 to prior U.S. non-provisional patent application Ser. No.12/242,144 entitled, “PLIANT MECHANISMS FOR EXTRACTING POWER FROM MOVINGFLUID,” filed Sep. 30, 2008, which in turn is a Continuation of andclaims priority under 35 U.S.C. §120 to U.S. non-provisional patentapplication Ser. No. 12/150,910 entitled, “Power generator forextracting power from fluid motion,” filed May 1, 2008, which in turn isa Non-Provisional of and claims priority under 35 U.S.C. §119 to U.S.provisional patent application Ser. No. 60/926,984 filed May 1, 2007.

All of the aforementioned applications are expressly incorporated hereinby reference.

BACKGROUND

The kinetic energy of a moving current of fluid has been harnessed bymankind for thousands of years. The first such mechanisms were used toperform kinetic energy-intensive tasks such as grinding grain or raisingwater from a river. Since the invention of the electromagneticgenerator, this kinetic energy of moving fluid has been converted intoelectrical energy, for distribution and consumption by all manner ofelectrical-energy-powered devices.

The raising of water from a river to a higher elevation for humanconsumption or for the irrigation of fields is one of the oldestrecorded uses of hydrokinetic energy. One such ancient mechanism isknown as a noria, in which jugs or buckets are fixed to a water wheel.The jugs fill when submerged, and then empty into an aqueduct near theuppermost position along the wheel's rotation. In such a device, theriver provides both the water and the energy required to move the waterto a desired location.

Other methods for moving water have been developed over the centuriessuch as the hydraulic ram and wind-powered pumps, but today pumpspowered by an electric motor or internal combustion engine usuallyperform such functions.

SUMMARY

Compliant or “pliant” elements of the embodiments described herein maybe assembled with force-induced deformations in the form of planarperturbations analogous to degenerate energy states. FIG. 1A illustrateshow aspects of some elements of implementations may be created viaforce-induced deformations in the form of planar perturbations in oneembodiment. The mechanisms may be created by applying force to aflexible article comprised substantially of elastic material to createdeformations in the material 1001 into which these forces are locked-inas potential energy in the deformations 1002. The mechanisms may beanchored in moving fluid 1003 whereupon the energy in the moving fluidexcites the deformations in the elastic material 1004. The energytransferred from the moving fluid into excitations in the elasticmaterial may be harnessed to perform work such as pumping or generatingelectricity 1005.

While the term “elastic” may be used to describe the material propertiesof elements of the flexible articles in these disclosures, flexiblearticles may, in another embodiment, be comprised primarily of rigid butarticulated materials, such as may have a substantially continuouscontact surface.

Aspects of the various implementations described herein facilitate thepumping of fluid from source to destination using the kinetic energyavailable in the fluid source itself, so long as the fluid source ismoving. Compliant, or pliant elements may also have several advantagesover, for example, a traditional noria that include at least potentiallygreater efficiency and less expense, and in some implementations theabsence of any articulated moving parts, resistance to impact damagefrom water-born objects, resistance to becoming tangled in plants orother water-born objects, and a more gentle physical interaction withfish and other aquatic animals.

The pumping mechanisms of compliant elements can also be configured togenerate electricity, whereby the kinetic energy of the fluid flowingthrough the pump is harnessed by an electromagnetic generator. Similaradvantages of the compliant electricity generation elements of thisinvention exist as those which apply to the pump implementations. Inaddition, the electricity generation elements are suitable for“free-flow” hydro applications which do not require the costly andenvironmentally impactful construction of dams across waterways.

The various compliant elements described herein may be configured toperform work such as to pump fluid for the purpose of moving it from oneplace to another, or pump fluid for the purpose of generatingelectricity. The energy to power these pumps may be provided by thekinetic energy of the moving fluid in which these elements are secured.

According to one implementation, pliant elements or mechanisms arefabricated from deformed flexible ribbons of material configured so asto change shape under forces exerted by the flow of fluid moving acrossor through the mechanisms. One or more undulations are created in theflexible material during fabrication. The undulations may be created bytaking a ribbon of flexible material, and applying a force to createundulations in the material, and then using at least one restrainingcomponent, or deformation-retention component, to prevent the ribbonfrom returning to its original unstrained state. The ribbons are securedto these restraining components via crenated strips which exhibithyperbolic geometry.

In an implementation, the undulations of the mechanisms run parallel tothe flow of the current in the moving fluid and the mechanisms aresecured to a substrate or other immovable object preventing them frombeing carried away with the current. Fluid moving past or through themechanisms exerts forces on the undulations of the ribbons, exciting theundulations and/or causing the undulations to travel down the ribbon inthe direction of the moving current. Through a variety of meansdescribed below, the traveling undulations of the ribbons are convertedinto pumping action on fluid captured in the mechanisms.

According to an implementation, pliant mechanisms are comprised of adouble layer of flexible ribbon material placed with planes parallel toone another and fixed to each other longitudinally but with a spacebetween the two layers, which may be referred to as the interstitialspace. A force is applied to the double ribbon to form undulations asabove. The undulations cause the respective layers of the double-layeredribbon to be closer together or further apart in a periodic manner thatcorresponds with the positions of the undulations, creating pocketsalong the interstitial space. As the undulations move along the lengthof the double ribbon under the forces of the moving fluid, the pocketsof interstitial space move with them.

In a pump implementation, the upstream end of the double-layered ribbonis open to incoming ambient fluid allowing fluid to enter theinterstitial space where it becomes enclosed in an interstitial pocketand transported along the length of the double-layered ribbon. Areservoir at the downstream end of the double-layered ribbon collectsthe pockets of fluid as they arrive and diverts the fluid along at leastone hollow conduit.

In a generator implementation, the upstream end of the double ribbon isclosed to ambient fluid but open to at least one conduit filled withfluid in a closed-loop system. Fluid from the conduit fills the firstpocket of interstitial space at the upstream end of the double ribbonand exits through a reservoir at the downstream end of the doubleribbon, to be transported via at least one conduit back to the upstreampocket of interstitial space, and so on. A turbine may be placed at alocation along the conduit to extract power from the moving fluidcycling through the conduit.

In another set of implementations, three or more undulatingsingle-layered or double-layered ribbons, which are each attached alongtheir outer edges to a rigid restraining member via crenated strips, areattached to each other along their inner edges via an inner connectingstrip so that the three respective inner crenated strips form a trianglein cross section (where three undulating ribbons are utilized). As thewaves undulate in unison, the triangle rotates partially clockwise andcounterclockwise, and the triangle expands and contracts in area, whichis to say that the summed lengths of the sides of the triangle increaseand decrease. Through a variety of valve mechanisms described herein,the expansion and contraction of the triangles creates a peristalticpump action which transports fluid, either for the purpose of drawing inambient fluid and pumping it to a desired location in open-loopimplementations, or for the purpose of powering an electromagneticgenerator in closed-loop implementations.

In another implementation, two, three or more, undulating ribbons areconnected longitudinally along their inner edges to a central elasticcoil. An implementation using three undulating ribbons is describedherein for illustrative purposes only and it is to be understood thatother configurations with more or less than three ribbons are possible.If a restrained coil is twisted in the rotational direction of thespiral of the coil, the coil will become shorter in length and/ornarrower in diameter, depending on how the coil is restrained. Likewise,if the coil is twisted in a direction opposite to the rotationaldirection of the spiral or coil, the coil will lengthen and/or increasein diameter, depending on how the coil is restrained. The threeundulating ribbons in the implementation are affixed to a central coilso that as the undulations travel along the length of the mechanismparallel to the flow of fluid, the central coil will be twistedclockwise and counterclockwise, causing its diameter to increase anddecrease, creating a peristaltic effect which moves fluid along acentral core, for the purpose of pumping ambient fluid in an open-loopsystem, or for the purpose of powering a turbine to generateelectricity.

It is to be understood that the elements described herein facilitatesignificant implementation flexibility/customization depending on avariety of factors including the requirements of a particularapplication. Furthermore, the various implementations described canfunction individually or be affixed to one another in scalable multiplearrays. In the pliant generating elements, the pumping action ofmultiple arrays can be summed to create higher fluid pressures moresuitable for powering conventional turbines. Accordingly, a large areaof fluid interacts with large areas of flexible ribbons which are thekinetic energy-receiving components of the mechanisms. Therefore, thesemechanisms take energy dispersed in a relatively large volume of movingambient fluid and concentrate that energy into a small volume of movingfluid at increased speed or pressure relative to the flowing ambientfluid.

For the sake of brevity and to facilitate visualization andcomprehension of particular implementations and embodiments of themechanisms described, the word “water” is used in the detaileddescription of these disclosures instead of the word “fluid”. It is tobe understood that all implementations utilizing the mechanismsdescribed herein are operable to transport and/or be driven by a widevariety of liquids, gases or any other substances exhibiting fluidicbehavior.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1A illustrates how aspects of some characteristics of some elementsof implementations may be created via force-induced deformations in theform of planar perturbations in one embodiment;

FIG. 1B illustrates one method for assembling a crenated strip in oneembodiment;

FIG. 1C illustrates how a single layered flexible ribbon may be formedin an embodiment;

FIGS. 2-3 illustrate how a crenated strip may be formed in anembodiment;

FIGS. 4-5 illustrate how a frond may be combined with crenated strips,in an embodiment;

FIG. 6 illustrates a pressure differential across wave undulations underoperation of a frond in an embodiment;

FIG. 7 illustrates the how a double layered ribbon may be formed in anembodiment;

FIGS. 8-9 illustrate a method of forming double crenated strips in anembodiment;

FIGS. 10-11 illustrate how a double-layered frond unit may be formed inan embodiment;

FIGS. 12A and 12B illustrate how pockets may be created by deformingdouble layers of flexible ribbon in elevation and perspectiverespectively in an embodiment;

FIGS. 13A and 13B illustrate an alternative way pockets may be createdby deforming double layers of flexible ribbon which are affixed to oneanother in another embodiment;

FIG. 14 illustrates a longitudinal cross section through a doublelayered frond implementation under operation;

FIG. 15 illustrates a longitudinal cross section through another doublelayered frond implementation under operation utilizing connectingstrips;

FIG. 16 illustrates a schematic cross section through the double layeredfrond implementation illustrated in FIG. 14;

FIG. 17 illustrates a schematic cross section through the double layeredfrond implementation illustrated in FIG. 15;

FIGS. 18A-E illustrate cross section cuts through a double layered frondimplementation with crenated strips that are substantially fixed intheir cross-sectional dimensions under operation;

FIGS. 19A-E illustrate cross section cuts through a double layered frondimplementation in which the crenated strips are substantially elastic intheir cross-sectional dimension and the ribbons are substantially fixedin their cross-sectional dimension under operation;

FIGS. 20A-E illustrate cross section cuts through a double layered frondimplementation where the cross-sectional dimensions of the ribbons andcrenated strips both vary under operation;

FIG. 21 illustrates positions within the cycle of operation that thesection cuts of FIGS. 18A-E, FIGS. 19A-E and FIGS. 20A-E are taken inone implementation;

FIG. 22A illustrates the double layered frond implementation of FIGS.18A-E in elevation;

FIG. 22B illustrates a perspective view of FIG. 22A;

FIG. 23A illustrates the double layered frond implementation of FIGS.19A-E in elevation;

FIG. 23B illustrates a perspective view of FIG. 23A;

FIGS. 24A-C illustrate cross-section cuts through a double-layered frondimplementation during one quarter of a cycle of operation;

FIG. 24D illustrates the locations within the wave bulge undulationcycle at which the section cuts of FIGS. 24A-C were taken.

FIGS. 25A-C illustrate cross-section cuts through a double layered frondimplementation with an auxetic interstitial structure, during onequarter of a cycle of operation;

FIG. 26 illustrates the locations within the cycle of operation at whichthe section cuts of FIGS. 25A-C are taken in one implementation;

FIG. 27 illustrates an auxetic hexagon in one implementation;

FIGS. 28-29 illustrate behavior of an auxetic hexagon structure in oneimplementation;

FIGS. 30A-C illustrate cross section cuts through a double layered frondimplementation in which ribbons are substantially non-elastic incross-sectional dimension and remain constant in cross-sectionaldimension under operation with an extruded parallelepiped-likeinterstitial structure;

FIG. 30 D illustrates the locations within the wave undulation cycle atwhich the section cuts of FIGS. 30 A-C are taken;

FIGS. 31A-D illustrate aspects of a double layered frond implementationwhereby the second interstitial structure will decrease in one directionwhen forces are exerted upon it in another direction;

FIG. 32 illustrates a double-layered frond pump implementation securedin a flowing stream of water in one embodiment;

FIG. 33 illustrates a frond pump implementation, in which water iscollected in a flexible reservoir;

FIG. 34 illustrates a frond pump implementation in which water collectedis pumped along a flexible tube;

FIG. 35 illustrates methods for assembling and implementing thedouble-layered frond mechanisms in some implementations;

FIG. 36A illustrates an asymmetric frond in an embodiment;

FIGS. 36B-C illustrate an asymmetric frond unit implementation;

FIGS. 37A-E schematically illustrate a sequence of end-on views of anasymmetric frond unit during one half of a cycle of operation in anembodiment;

FIGS. 38A-E illustrate the sequence illustrated in FIGS. 37A-E from aperspective view showing the entire asymmetric frond unit in anembodiment;

FIG. 39 illustrates the positions that the downstream-ends of theasymmetric fronds take within the wave bulge undulation cycle as shownin FIGS. 37A-E and FIGS. 38A-E in one implementation;

FIGS. 40-41 illustrate the first triangular core in some single-layeredfrond implementations;

FIG. 42 illustrates a series of elastic triangular membranes along atriangular core in one single-layered frond implementation;

FIG. 43 illustrates a schematic section through one pump implementationof one single-layered frond mechanism;

FIGS. 44A-C illustrate the behavior in a single-layered frondimplementation of elastic triangular membranes at three moments of timecorrelating to three positions within one quarter of a wave bulge cyclein one embodiment;

FIG. 45 illustrates three points in one quarter of a wave bulge cyclethat correspond with FIGS. 44 A-C in one implementation;

FIGS. 46A-D illustrate four cross-sectional views of a triangular coreand membrane in one single-layered frond implementation;

FIG. 47 illustrates the corresponding positions within one quarter of awave undulation cycle that the cross-sections of FIGS. 46 A-D were takenin one implementation;

FIG. 48 schematically illustrates a single-layered frond implementationin operation in which the pumping action of an asymmetric frond unitpowers a turbine in one implementation;

FIGS. 49-50 illustrate exploded three dimensional views of anothersingle-layered frond pump implementation utilizing an elastic core tube;

FIG. 51 is a schematic illustration of a pump implementation inoperation utilizing an elastic core tube;

FIG. 52 is a schematic illustration of a generator implementation inoperation utilizing an elastic core tube;

FIGS. 53A-C illustrate a first triangular core incorporating atriangular valve mechanism in one single-layered frond implementation;

FIGS. 54A-D illustrate end-on views of a triangular valve mechanism atfour points in time under operation in one single-layered frondimplementation;

FIGS. 55A-D illustrate side-on views of a triangular valve mechanism atthe corresponding four points in time under operation illustrated inFIGS. 54A-D in one single-layered frond implementation;

FIG. 56. schematically illustrates a single-layered frond pumpimplementation in operation utilizing a triangular valve mechanism inone embodiment;

FIG. 57 schematically illustrates a single-layered frond implementationsimilar to the pump implementation illustrated in FIG. 56 but powering aturbine in one embodiment;

FIG. 58A illustrates another single-layered-frond pump implementationsimilar in design and operation to the third single-layered-frond pumpimplementation illustrated in FIG. 56 but utilizing inner connectingstrips in one embodiment;

FIG. 58B is a view of the first triangular core looking down itslongitudinal axis illustrating how the inner connecting strips form aninverted hexagon in one implementation;

FIG. 59A illustrates another single-layered frond generatorimplementation with the addition of inner connecting strips and tube inone embodiment;

FIG. 59B illustrates a method for assembling and implementingsingle-layered frond mechanisms in one embodiment;

FIG. 60A is a wire-frame illustration of a spiral valve embodimentsutilizing three connected flexible ribbons, as viewed down thelongitudinal axis of the mechanism in one implementation;

FIG. 60B is a wire-frame illustration of a spiral valve embodimentsutilizing three connected flexible ribbons, as viewed in elevation inone implementation;

FIG. 61 illustrates two examples of methods for the fabrication of thespiral valve implementations in some embodiments;

FIG. 62 illustrates an aspect of one spiral valve implementation wherebyone or more undulating ribbons are secured to a coil in one embodiment;

FIG. 63 illustrates an aspect of a spiral valve implementation wherebythe coil is sequentially wound and unwound by applied forces in oneembodiment;

FIG. 64 illustrates a schematic cross-section through an implementationutilizing a spiral valve mechanism;

FIG. 65A-E illustrate schematic cross-sections through an implementationutilizing a spiral valve mechanism at different moments duringoperation;

FIGS. 66-70 illustrate various components of a spiral valveimplementation;

FIG. 71 illustrates a spiral valve implementation incorporating thevarious components illustrated in FIGS. 66-70 with flexible ribbons;

FIGS. 72A-C illustrate a spiral valve implementation with internalradial fins or arms attached to the elastic coil at points tangent tothe circumference of the elastic coil;

FIGS. 73A-C illustrate a spiral valve implementation with radial rigidarms secured via rigid sliding connections to the triangular core;

FIG. 74 is a wire-frame illustration of a component of a spiral valveimplementation utilizing radial fins or arms to connect the secondtriangular core to the elastic coil;

FIG. 75 is a wire-frame illustration of a component of a spiral valveimplementation looking down the center of the longitudinal axis of alength of second triangular core utilizing radial fins or armsconnecting the second triangular core to the elastic coil;

FIG. 76 is a wire-frame illustration of a component of a spiral valveimplementation looking down the center of the longitudinal axis of alength of second triangular core utilizing rigid radial arms;

FIG. 77 illustrates a wire-frame perspective of assembled components ofa spiral valve implementation showing a section equivalent to one wavebulge undulation;

FIG. 78 is a wire frame elevation of the same portion of spiral valvemechanism shown in FIG. 77 viewed perpendicular to the longitudinal axisof the mechanism, showing certain elements of the mechanism in oneimplementation;

FIG. 79 illustrates the elevation of FIG. 78 with additional componentsin one implementation;

FIG. 80 illustrates a spiral valve implementation mechanism in aposition it may assume when secured in a stream of fluid in oneembodiment;

FIG. 81 illustrates a spiral valve implementation mechanism secured in astream of moving fluid in one embodiment;

FIG. 82 illustrates a cross-section cut through a spiral valveimplementation mechanism secured in a flowing stream of fluid in oneembodiment;

FIG. 83 is a schematic illustration of a spiral valve implementationmechanism utilized as a pump showing the circulation of pumped water orfluid through the mechanism in one embodiment;

FIG. 84 is a schematic illustration of a spiral valve implementationmechanism utilized as a generator showing the circulation of water orfluid in one embodiment;

FIG. 85 illustrates a spiral valve implementation mechanism utilizingsix ribbons and placed within a tube of flowing fluid in one embodiment;

FIG. 86 is a diagrammatic representation of the internal energy state ofa deformation within a flexible material and the internal energy stateof a deformation-retaining component in one implementation;

FIG. 87 is a diagrammatic representation showing an external forceexerted by a moving ambient fluid upon a deformed flexible material,transferring these forces onto a second fluid in one implementation;

FIG. 88 illustrates how two or more electrodes may be connected to adeformed electroactive material in an implementation in which materialstrain is converted into electrical energy; and

FIGS. 89-93 diagrammatically illustrate several ways that the energy ofa moving fluid may be harnessed via flexible components of mechanisms invarious implementations.

DETAILED DESCRIPTION

Pliant, or “compliant” elements or mechanisms extract energy from amoving body of water and use that energy to do work such as pump waterfrom the moving body of water, or to pump water through a closed-loopsystem to power an electric generator. In the descriptions herein forvarious embodiments and/or implementations, numerous specific detailsare provided, such as examples of components, elements and/ormechanisms, to provide a thorough understanding of implementationsdescribed herein. However, it is to be understood thatembodiments/implementations may be practiced without one or more of thespecific details, through interchanging aspects of the illustratedimplementations/embodiments, or with other apparatuses, systems,assemblies, methods, components, materials, parts, and/or the like.

At least three groups of pliant elements are described herein forillustrative purposes. The first group includes mechanisms incorporatingdouble-layered fronds; the second group includes mechanisms comprised ofsingle-layered fronds; and the third group includes mechanismsincorporating spiral valves.

Double-Layered-Frond Mechanisms.

FIG. 1C illustrates aspects of creating a component common to severalimplementations described herein, namely the flexible deformed ribbon 2.The flexible ribbon is straight in its relaxed state 1. At least a firstforce 3 is applied to the ribbon in a manner so as to create one or aseries of undulations along its length. The deformations are the resultof the internal energy state of the material imposed by this first force3.

FIGS. 2-3 illustrate aspects of creating another component common tomany of the implementations described herein, the crenated strip 6. Onemethod for creating a crenated strip with the described morphology andinternal energy state is as follows: An arc-shaped piece of flexible orelastic sheet-like material 5 is deformed with at least a second force 7until the outer arc of the strip 8 a and the inner arc of the strip 8 bbecome equal in length, at which point the inner arc 8 b of the strip isin tension, and the outer arc 8 a of the strip is in compression causingthe strip to take on a hyperbolic geometry with a “crenated”, or ruffledappearance.

FIG. 1B illustrates one method for assembling a crenated strip in animplementation whereby an arc-shaped strip of elastic sheet-likematerial 1006 has forces applied to it 1007 so that the inside edge ofthe arch-shaped strip is straightened, creating a crenated strip 1008.The straight edge of the crenated strip may be secured to a rigid ortensile member 1009 to lock-in the applied forces as potential energy.

A deformed ribbon 2 is fixed to two crenated strips 6 along its outerlongitudinal edges creating a frond 9. The first force 3, which has beenapplied to the ribbon 1 and the second force 7, which has been appliedto the pre-strained crenated strips 5, are held as potential energywithin the frond 9 by the first restraining, or deformation-retentioncomponents 10, such as rigid tubes or members FIGS. 4-5. The frond 9 isnow in its strained or “charged” state. The undulations are expressionsof the internal energy state of the frond, so will remain as long as thefirst restraining components, or deformation-retention components 10remains affixed to the frond 9. Therefore, additional forces applied tothe frond 9 can change the relative positions of the undulations withinthe frond 9 but not the presence of the undulations in some positionwithin the frond 9.

When the frond 9 is secured in a moving stream of fluid so that thefrond is fixed in place and does not travel with the fluid, and so thatthe length of the frond 9 runs substantially parallel to the directionof moving fluid 11, the pressure of the fluid adjacent to portions ofthe frond that face obliquely upstream 4 a will be greater than thepressure of the fluid adjacent to portions of the frond that faceobliquely downstream 4 b, FIG. 6. These pressure differentials cause thepositions of the undulations to move along the length of the frond inthe direction of the moving fluid 11. The kinetic energy of the movingwater is therefore transferred into the movement of undulations downalong the frond 9. Work is extracted from the movement of theundulations to power the mechanisms embodied herein. The number ofundulations is a property of the way the material receives strains andthe internal energy state of the frond 9. Therefore, if the kineticenergy of the moving water 11 pushes an undulation off of one end of thefrond 9, another undulation will form at the opposite end of the frond9.

In several implementations, the flexible ribbon 2 may be configured as adouble-layer, with the respective layers being connected to each otherlongitudinally but with interstitial space 2 a in between the twolayers. In these double-layered frond 9 a implementations, the flexibleribbons 2 may be connected to each other indirectly via crenated strips6 to the first restraining components 10, or may be connected to eachother directly via intermediate flexible connections 12 (FIG. 17), whichin turn connect to a crenated strip 6, which in turn is connected to thefirst restraining components 10. FIGS. 7-11 show how a double-layeredfrond 9 a may be formed and connected via crenated strips 6 to the firstrestraining component 10.

In double-layered frond 9 a implementations where the flexible ribbons 2are connected to each other via two crenated strips 6 to the firstrestraining components 10, the two crenated strips may be separated fromeach other in a manner that matches the separation of the two flexibleribbons 2 and therefore make contact with each other as the two flexibleribbons 2 make contact, and separate as the two flexible ribbons 2separate, being fixed to the two flexible ribbons 2 along theirundulating longitudinal edges. Along their other, non-undulating edgesthe crenated strips 6 make contact with one another at their place ofcontact with the first restraining component 10, or come close togetherso that the interstitial space between the crenated strips 6 isnarrowest along their straight edges.

FIGS. 12A and 13A illustrate aspects of how pockets 13 may be created inthe interstitial space 2 a between the ribbons 2 of the double-layeredfrond 9 a implementations. In FIG. 12A a first force 3 is applied to tworibbons 2 of a flexible sheet-like material separated from each other bya small interstitial space 2 a causing them to bend and deform toaccommodate this force 3. The radius of the two curves formed by the tworibbons 2 are equal and one curve lies above the other, therefore thedistance between the two ribbon 2 layers is greatest at the peak of thecurve. Therefore, a pocket 13 is created in the interstitial space 2 abetween the two ribbons 2.

In FIG. 13A the interstitial space between the two ribbons 2 is occupiedby an interstitial material or structure 14 fixed to the inside faces ofboth ribbons 2 and which can be readily compressed or stretched on theaxis perpendicular to the plane of the ribbons 2. This configuration canbe thought of as analogous to a three-layered laminated material inwhich the two outer layers are flexible perpendicular to the plane ofthe material but which can be stretched or compressed only minimally inthe longitudinal direction parallel to the plane. In this analogy, thethird, inner layer connecting the two outer layers could be a materiallike soft foam rubber. In this analogous configuration, the two outerlayers, being bound to one another and unable to shift substantially inthe longitudinal direction, will press closer together at the greatestpeak of the curve 15, and separate from one another one half way up thepeak, creating pockets 13 at those locations. FIGS. 12B and 13B arethree dimensional representations of FIGS. 12A and 13A.

FIG. 14 illustrates a longitudinal cross-section through adouble-layered frond 9 a configured with a series of undulations withinterstitial pockets 13 at the peak amplitude of the bulge deformationseither side of the wave undulation's neutral axis, in accordance withthe characteristics illustrated in FIGS. 12A and 12B. When secured inplace, the current of water 11 passing across the double-layered ribbons2 causes the bulge undulations to travel down along the double-layeredribbons 2 in the direction of the current, and therefore the positionsof the interstitial pockets 13 will travel along the frond 9 a with thebulge undulations. If the interstitial space between the double-layeredribbons 2 at the upstream end of the frond is open to the water of theflowing current 11, ambient water 16 may enter the interstitial space atthe maximum wave amplitude during which the interstitial 2 a space is atits greatest. This water will become enclosed in an interstitial pocket13 which will travel along the frond in the direction of the movingwater current, and exit 17 at the downstream end of the double-layeredfrond 9 a.

FIG. 15 shows a longitudinal cross-section through a double-layeredfrond 9 a configured with a series of undulations with interstitialpockets 13 that occur at the neutral axis respectively, in accordancewith the characteristics described above and illustrated in FIGS. 13Aand 13B. (The interstitial structure 14, which allows the passage ofwater is not shown in FIG. 15 for purposes of graphic clarity, but willbe described subsequently and is illustrated in FIGS. 25A-C and FIGS.30A-C). The forces of water in the moving current 11 move theinterstitial pockets 13 along the frond as described above for theimplementation illustrated in FIG. 14, so the action of theimplementations illustrated in FIG. 14 and FIG. 15 are similar. Adifference occurs in where during the cycle of wave undulations thepockets are created.

As above, each ribbon 2 of the double-layered frond 9 a may be attacheddirectly along both longitudinal edges to crenated strips 6, whichthemselves are attached to the first restraining component 10. Such anarrangement is utilized in the double-layered frond 9 a implementationwith pockets at maximum amplitude as illustrated in FIG. 14. Across-section of this arrangement is shown in FIG. 16. Alternatively,the longitudinal edge of each ribbon 2 of the double-layered frond 9 amay be connected to one another via intermediate flexible connections12, each of which is connect to a single crenated strip 6 which in turnconnects to the first restraining component 10 as shown in FIG. 17.

FIGS. 16, 17 also illustrate how cross section cuts throughdouble-layered frond implementations may take the form of elongatehexagons: In FIG. 16 the sides of the hexagon are comprised of tworibbons 2 and four crenated strips 6. In FIG. 17 the sides of thehexagon are comprised of two ribbons 2 and intermediate flexibleconnections 12.

The behavior of the frond 9 or double-layered frond 9 a under operationis subtle and will vary depending on a number of factors including therelative elasticity of ribbons 2, crenated strips 6 and, where present,the intermediate flexible connections 12 among other factors. FIGS.18A-E and FIGS. 19A-E are schematic diagrams showing five cross-sectioncuts viewed from a certain direction 2201 and 2301 respectively, of twoslightly different frond 9 configurations during one half a cycle ofoperation, starting at maximum amplitude of the wave bulge, decreasingto zero amplitude, and increasing again to maximum amplitude on theopposite side of the neutral axis. FIG. 21 illustrates where in the wavecycle, or bulge deformation cycle, these corresponding section cuts weretaken for the two respective figures above. Dotted lines have been addedto FIGS. 18A-E and 19A-E connecting the same points in the successivesection cuts to show how the locations of these points change duringoperation.

The summed cross-sectional dimension, which is the width of a ribbon 2plus the width of two fronds 6, varies during operation, being at itsmaximum at the maximum amplitude of deformation, and being at itsminimum at the neutral axis of the wave, at which point the ribbons 2and crenated strips 6 approximate a straight line in cross-section.(FIGS. 18C and 19C). Several implementations are described herein whichfacilitate or accommodate this behavior.

FIGS. 18A-E illustrate an implementation with crenated strips 6 that aresubstantially fixed in their cross-sectional dimension 18. Therefore,the cross-sectional dimension 19 of the ribbon 2 in this implementationmust change during operation, and therefore must be substantiallyelastic in cross-sectional dimension. In double-layered frond 9 aimplementations incorporating intermediate flexible connections 12, thesummed cross-sectional dimension 19 of the ribbons 2 plus intermediateflexible connections 12 must change during operation, being maximum inFIG. 18A, E and minimum in FIG. 18C.

FIGS. 19A-E show an implementation in which it is the crenated strips 6that are substantially elastic in their cross-sectional dimension 18,whereas the ribbons 2 are substantially fixed in their cross-sectionaldimension 19. Therefore the cross-sectional dimension 18 of the crenatedstrips 6 must change during operation. In double-layered frond 9 aimplementations incorporating intermediate flexible connection 12 thecross-sectional dimension 18 of the fronds 6, or the summedcross-sectional dimension of the fronds 6 plus intermediate flexibleconnections 12, must change during operation, being maximum in FIG. 19A,E and minimum in FIG. 19C.

FIGS. 20A-E illustrate yet another configuration, whereby thecross-sectional dimensions 19 of the ribbon 2 and the cross-sectionaldimension 18 of the crenated strips 6 both vary under operation, becauseboth the ribbon 2 and crenated strip 6 are substantially elastic intheir cross-sectional dimension. Therefore, both the cross-sectionaldimension 19 of the ribbon 2 and cross-sectional dimensions 18 of thecrenated strips 6 are at their shortest at the neutral axis of the wavedeformations (FIG. 20C). FIG. 21 illustrates positions within the cycleof operation that the section cuts of FIGS. 18A-E, FIGS. 19A-E and FIGS.20A-E are taken in one implementation.

The morphology taken by the implementation shown in FIGS. 18A-E isillustrated as an elevation in FIG. 22A. The morphology of theimplementation shown in FIGS. 19A-E is illustrated as an elevation inFIG. 23A. A perspective view of the implementation illustrated in FIG.22A is shown in FIG. 22B, and a perspective view of the implementationillustrated in FIG. 23A is shown in FIG. 23B.

FIGS. 24A-C shows a cross-section through a double-layered frond 9 aimplementation during one quarter of a cycle of operation, during whichthe bulge deformation changes from maximum to minimum amplitude of thewave bulge cycle, and the interstitial pocket 13 changes from maximumvolume at maximum amplitude, to minimum volume at minimum amplitude. Inthe implementation shown in this illustration, both the ribbons 2 andcrenated strips 6 are substantially elastic in their cross-sectionaldimensions. (FIGS. 20A-E). The cross-sectional dimensions 18 of thecrenated strips 6 and the cross-sectional dimensions 19 of the ribbons 2decrease steadily between position of operation as shown in FIG. 24A andposition of operation as shown in FIG. 24C.

FIG. 24D indicates the locations within the wave bulge undulation cycleat which the section cuts of FIGS. 24A-C are taken.

FIGS. 25A-C show yet another double-layered frond 9 a implementationduring one quarter of a cycle of operation, in which the interstitialspace 2 a is occupied by an interstitial structure 14. FIG. 26 indicatesthe locations within the wave bulge undulation cycle at which thesection cuts of FIGS. 25 A-C are taken.

The components 22 of this interstitial structure 14 are comprised of amaterial enabling the components 22 to flex at their joints, allowingthe interstitial structure as a whole to expand or contractperpendicular to the plane of the longitudinal axis of the frond 9 a.The material comprising the components 22 is highly-elasticperpendicular to the longitudinal axis of the frond 9 a. The components22 of this interstitial structure 14 are fixed to the internal faces ofthe crenated strips 6 and ribbons 2 and take the form of continuousextrusions, or channels 23, running parallel to the longitudinal axis ofthe double-layered frond 9 a. Water 16 entering the upstream end of thedouble-layered frond 9 a passes along the channels 23 created by theseextruded components 22. Under operation, the cross-sectional dimensionof these channels 23 expands and contracts perpendicular to the planesof the crenated strips 6 and ribbons 2. The positions of the regions ofexpansion and contraction in the double-layered frond 9 a move parallelto the flow of the water current 11, pushing water in the channels 23down along the frond, where the water exits 17 the double-layered frond9 a as shown in FIG. 14.

The action of the double-layered frond 9 a described above andillustrated in FIGS. 25A-C are facilitated in one implementation byutilizing characteristics of auxetic structures. Auxetic materials arematerials with a negative Poisson's ratio, which is to say that when thematerial is stretched in one direction, it does not shrink in the otherdirection but instead expands in this other direction also. The term“auxetic” is applied to materials but can also apply to structures, onevariation of which is the so-called Hoberman Sphere. The auxeticstructures as employed in this implementation and shown in FIGS. 25A-Cmay utilize the inverted hexagon 24, also referred to as the auxetichexagon FIG. 27. When multiple auxetic hexagons 24 are configured in amanner as shown in FIG. 28, the resulting auxetic structure 25, whenstretched by a force 26 in one dimension will also stretch in anotherdimension 27, FIG. 29.

The components 22 of the interstitial structure 14, in combination withthe fronds 6 and ribbons 2, comprise the auxetic structures 25 of thisimplementation. These components 22 take on the form of auxeticstructures 25 in cross section, whereby these structures are extrudedlongitudinally along the length of the double frond 9 a forming channels23 down which water may flow. The inclusion of auxetic structuresoccupying the interstitial space 2 a facilitates the expansion andcontraction of the interstitial pockets 13, and thus the channels 23, inthe following manner: When the crenated strips 6 and double-layeredribbons 2 increase in cross-sectional dimension, their action will causethe auxetic structures 25, which they are a part of, to increase indimension perpendicular to the axis of the double-layered frond, thusexpanding the space between the two ribbon 2 layers and two crenatedstrip 6 layers, and thus further facilitating the expansion of thepockets 13 of the interstitial space 2 a.

FIGS. 30A-C illustrates an implementation which combines characteristicsof auxetic structures as illustrated in FIGS. 25A-C and FIG. 28 with theconfiguration illustrated in FIG. 19A-E in which the ribbons 2 aresubstantially non-elastic in cross-sectional dimension and remainconstant in cross-sectional dimension under operation. In thisimplementation, the interstitial space 2 a between the double-ribbons 2is at its minimum where the bulge deformation reaches its maximumamplitude under operation, and the interstitial space 2 a between thedouble-ribbons 2 is at its maximum where the bulge deformation is atzero amplitude at the neutral axis of the bulge undulations underoperation, as shown in FIG. 15. The double ribbons 2 are of a flexiblematerial but are minimally elastic in their cross-sectional dimension,which is to say that the material they are comprised of cannot besubstantially stretched in plane, so that the ribbons 2 remainessentially constant in width as they flex and undulate perpendicular totheir planes under operation. The crenated strips 6 are also minimallyelastic, or non-stretchable, in their cross-sectional dimension.

For this implementation illustrated in FIGS. 30A-C the changes is summedcross-sectional dimension of the frond 9 under operation may beaccommodated entirely by the intermediate flexible connections 12. Theseintermediate flexible connections may be secured to the crenated strips6 and ribbons 2 via rotational or flexible hinged joints 28, 29. (Someimplementations may incorporate flexible joints instead of or inaddition to articulated joints throughout.) As the double ribbons 2 movefurther apart under operation, the ends of the intermediate flexibleconnections 12 which are attached 28 to the ribbons 2, move apart also,rotating about the axis of the point 28 where they attach to the ribbons2. Simultaneously the ends of the intermediate flexible connection 12that attach to the crenated strip 6 rotate about the axis of their pointof attachment 29 to the crenated strip 6.

FIG. 30D indicates the locations within the wave undulation cycle atwhich the section cuts of FIGS. 30A-C are taken.

In addition to being connected to each other via the intermediateflexible connections 12, the double ribbons 2 may also be connected toeach other via a second interstitial structure 14 a taking the form ofan extrusion that is connected longitudinally along the length of thedouble frond 9 a, and which takes the form in cross-section of anarticulated structure that mimics the profile of the intermediateflexible connections 12.

FIGS. 31A-D illustrate aspects of an implementation whereby the secondinterstitial structure will decrease in one direction when forces areexerted upon it in another direction: When a row of parallelograms 30are connected to one another and held in tension along one edge 31 and atensile force 32 is applied along the opposite edge in the oppositedirection, they will collapse together and the space 33 defined by theenclosure of each parallelogram will decrease in volume.

FIGS. 30A-C as described above, showing a series of cross-sectionsthrough an implementation of a double-layered frond 9 a, utilize adouble row of parallelograms, as viewed in cross-section. Theseparallelograms are extruded along the length of the frond as extrudedtorqued parallelepipeds. One side of each parallelogram is comprised ofa portion 34 of the ribbon 2, and each opposite side is comprised of aportion of one of two interstitial ribbons 35 which run through thecentral axis of the double-layered frond 9 a. The remaining two sides ofeach parallelogram are comprised of tertiary components 36 which attachto the inside face of one double-layered frond ribbon 2 and to one ofthe interstitial ribbons 35. These interstitial ribbons 35 are connectedalong one edge 36 a to a crenated strip 6. The crenated strips are heldin maximum tension during the maximum bulge deformation under operation,and will therefore be exerting a lateral force 32 pulling theparallelograms into their collapsed position as demonstrated in FIG.31D. The effect of the tension in the crenated strips 6 therefore is topull the two ribbons 2 together at maximum bulge amplitude. When tensionin the crenated strips 6 is at its minimum the parallelograms of theinterstitial structure 14 may be in their resting state, in which thetwo ribbons 2 of the double-layered frond 9 a are furthest apart.

FIG. 32 shows a double-layered frond pump implementation secured in aflowing stream of water 11 via a second restraining component 37, in theform of a post or rigid tube fixed to the bed of a river, tidal basin,or other immovable object 38. The second restraining component 37 may behinged about its longitudinal axis allowing it to swivel in the currentso that the double-layered frond 9 a remains approximately aligned withthe direction of the moving current. The second restraining component 37is fixed to the first restraining components 10. Under operation theupstream end of the double-layered frond 9 a is open to the ambientwater 16 from the flowing stream of water when the upstream end of thedouble-layered frond 9 a is deformed so as to create a pocket 13 orexpanded channels 23 in the interstitial space 2 a as described in thevarious implementations above. (FIGS. 14-15). As the pocket 13 movesdown the length of the double-layered frond 9 a, the water in the pocketis transported along the length of the double-layered frond 9 a andexits the downstream-end of the double-layered frond 9 a, where itenters a first reservoir 40 made of a flexible material, and then entersa first flexible tube 41, which diverts the pumped water 17 to a desireddestination.

FIG. 33 illustrates yet another implementation, in which water collectedin the flexible first reservoir 40 at the downstream end of thedouble-layered frond 9 a is transported along at least one firstflexible conduit 42 to another second flexible conduit 43 that runsalong the interior of one or both first restraining components 10, wheresaid first restraining components 10 are hollow. The water travelingalong the second flexible conduit 43 connects to a second flexible tube44 which diverts the water 17 to a desired destination.

FIG. 34 illustrates yet another implementation in which water collectedin the flexible first reservoir 40 is pumped along at least one fourthflexible tube 45 which is affixed to the surface of at least one of theflexible ribbons 2 and which passed along the surface of the ribbon 2 inthe opposite direction to the flow of ambient water 11, until it reachesthe second restraining component 37, which the fourth flexible tube 45attaches to or penetrates into, after which it joins at least one fifthflexible tube 46, through which exiting water 17 is transported to adesired destination.

FIG. 35 illustrates two methods for assembling and implementing thedouble-layered frond mechanisms in some implementations. In oneimplementation, two ribbons of flexible sheet-like material 3501 haveforces applied to create undulating deformations 3502. The two ribbonsare connected to four crenated strips 3504. The mechanism is anchored ina moving fluid 3507 and energy is extracted or work performed by themechanisms 3508. In another implementation, two ribbons of a flexiblesheet-like material 3501 have forces applied to create undulatingdeformations 3502. The two ribbons are connected to two intermediateflexible connections 3505. The intermediate flexible connections areconnected to two crenated strips 3506. The mechanism is anchored in amoving fluid 3507 and energy is extracted or work performed by themechanisms 3508.

In another implementation, electrical energy extraction from thedeformed dynamic undulations in the ribbons, and other elements of theabove mechanisms which flex in a periodic manner under operation, iswith the utilization of an electroactive material which exhibits anelectrical response to deformation. In such implementations of themechanisms described, two or more electrodes may be utilized to extractelectricity from the mechanisms.

Single-Layered-Frond Mechanisms.

By way of example only, a second embodiment of mechanisms may utilizesingle-layered fronds 9. Each frond 9 is comprised of a strainedflexible ribbon 2 and strained crenated strips 6. However, while in thedouble-layered frond implementations described above each ribbon isconnected to at least two crenated strips 6, one along each longitudinaledge of the ribbon 2, in the single-layered frond implementations eachribbon 2 may be fixed to only one crenated strip 6 along onelongitudinal edge of each ribbon 2.

The crenated strip 6 attached to this one edge of the ribbon 2 is fixedto the first restraining component, or deformation-retention component10. The opposite edge of the ribbon 2 is fixed to a connecting strip 47comprised of a sheet-like flexible material. In the process of fixingthis flexible sheet to the ribbon 2 the flexible sheet is deformedsubject to the first applied force 3 that is held as potential energy inthe ribbon 2 and thereby takes on an undulating hyperbolic geometrysimilar to that of the crenated strip 6. The ribbon 2, crenated strip 6and connecting strip 47 together comprise an asymmetric frond 48, FIG.36A.

At least three asymmetric fronds 48 may attached to one another alongthe respective longitudinal edges of each other's connecting strips 47,so that the connecting strips 47 of the three asymmetric fronds 48 takethe form of a triangle in cross section where three asymmetric fronds 48are utilized. The three asymmetric fronds 48 plus three firstrestraining components 10 together comprise an asymmetric frond unit 49,FIGS. 36B-C. The three asymmetric fronds 48 share a common axis whichruns substantially parallel to the direction of flowing water 11. Whenthe asymmetric frond unit 49 is secured in place in that flowing water11 so as not to be carried away in the current, the positions of theundulations within the ribbons 2 will travel down along the lengths ofthe ribbons 2, as described above (e.g. FIG. 6.)

The asymmetric frond unit 49 is configured so that each of itsasymmetric fronds 48 has the same number of wave undulations of equalamplitude. In addition, under operation the relative wave positions ofone asymmetric frond 48 are in-phase with the wave positions of theother two asymmetric fronds 48 in relation to the central axis of thefrond unit 49.

The asymmetric fronds 48 of the asymmetric frond unit 49 may be heldtogether additionally by at least one peripheral connecting structure 50which is affixed to all three asymmetric frond units 49 via the threefirst restraining components 10.

In one implementation the crenated strip 6 and ribbon 2 of theasymmetric frond 48 may be composed of a flexible sheet-like materialwhich allows deformation perpendicular to the plane of the sheet-likematerial. However, this material may also be substantially non-elasticin the direction parallel to the plane of this sheet-like material, justas a thin stainless steel ruler will readily flex perpendicular to itsplane, but resist substantial stretching when either end is pulled inopposite directions. By contrast, the connecting strips 47 in thisimplementation are comprised of a material that is highly elastic in thedirection parallel to the plane of the material.

FIGS. 37A-E schematically show a sequence of end-on views of anasymmetric frond unit during one half of a cycle of operation. The viewis taken from a position downstream of the asymmetric frond unit 49looking upstream at the end of the asymmetric frond unit 49. As the waveundulations move either to one side or the other of their neutral waveamplitudes, the triangle formed by the three joined connecting strips 47rotates partially clockwise or counter-clockwise about the longitudinalcentral axis of the asymmetric frond unit 49. Because the sheet-likematerial comprising the crenated strips 6 and ribbons 2 is substantiallynon-elastic in the direction parallel to the plane of the material, andbecause the sheet-like material comprising the connecting strips 47 ishighly elastic in the direction parallel to the plane of the material,under operation the diameter of this triangle expands and contracts in aperiodic manner. This occurs because the summed length of crenated strip6 plus ribbon 2 plus connecting strip 47 of each asymmetric frond 48varies under operation, but only the highly elastic connecting strip 47is able to change substantially in cross-sectional dimension. FIGS.38A-E illustrate the sequence illustrated in FIGS. 37A-E but from aperspective view showing the entire asymmetric frond unit 49.

FIG. 39 illustrates the positions that the downstream-ends of theasymmetric fronds 48 take within the wave bulge undulation cycle asshown in FIGS. 37A-E and FIGS. 38A-E.

FIGS. 37A-E can also be regarded as being illustrative of across-sectional cut through a single point in the asymmetric frond unit49 as viewed during one half cycle of operation, and correlating withmoments in the wave cycle as illustrated in FIG. 39: The cross-sectionallengths of the crenated strips 6 and ribbons 2 remain constant underoperation, while the cross-section lengths of the connecting strips 47vary under operation. The three connecting strips 47, each attachedalong one longitudinal edge to both of the other two connecting strips47, together constitute a first triangular core 51 which takes on theform of an extruded hollow triangle which twists clockwise andcounter-clockwise and which becomes narrower and wider in circumferenceFIGS. 40-41. The effect of wave undulations passing down the length ofthe asymmetric fronds 48 under operation is translated into a twistingperistaltic motion down the length of the first triangular core 51,which is where the pumping action of the single-layered frondimplementations take place.

FIG. 42 illustrates a series of highly elastic triangular membranes 52which may be secured to the inside faces of the connecting strips 47comprising the first triangular core 51. Within each of the elastictriangular membranes 52 is a circular opening 53. Under operation, asthe first triangular core 51 twists, expands, and contract with thepassing of undulations along the asymmetric fronds 48, the elastictriangular membranes 52 expand and contract, and the circular openings53 within these elastic triangular membranes 52 increase and decrease inradius.

FIG. 43 illustrates a schematic section through the first pumpimplementation of the single-layered frond mechanisms. An asymmetricfrond unit 49 is secured via its first restraining components 10 to athird restraining component 54 which takes the form of a hollow rigidpost or rigid tube which itself is fixed to the bed of a river, tidalbasin, or other immovable object 38. The third restraining component 54may be hinged about its longitudinal axis allowing the asymmetric frondunit 49 to swivel in the moving current so as to maintain a longitudinalaxis parallel to the moving current. The third restraining component 54is shown as protruding above the surface of the flowing water 55 forgraphic clarity. The asymmetric frond unit 49 is secured to the thirdrestraining component 54 via the first restraining components 10. Afifth hollow tube 56 passes along the length of the interior of thefirst triangular core 51 and penetrates and is secured to the thirdrestraining component 54. Where the diameter of the circular openings 53in the elastic triangular membranes 52 are at their minimum state, theinside edges of the circular openings 53 make contact with and applypressure to the surface of the fifth hollow tube 56. Ambient water 16from the flowing current of water 11 is able to enter at theupstream-end of the asymmetric frond unit through the space between thefirst triangular core 51 and the fifth hollow tube 56, when the diameterof the circular openings 53 in the elastic triangular membranes 52 aregreater than their minimum dimension.

As the undulations in the triangular core 51 are moved along theasymmetric frond unit 49 under the forces of the flowing water 11, aseries of pockets containing collected ambient water 57 will also passalong the length of the interior of the triangular core. The circularopenings 53, after allowing the ambient water 16 to enter at theupstream end of the first triangular core 51 during their phase ofgreater diameter, will contract and eventually make contact with thefifth hollow tube 56, creating a series of valves that direct waterthrough the first triangular core 51 in the direction of the flowingcurrent of water 11.

FIGS. 44A-C further illustrate the behavior of the elastic triangularmembranes 52 along the inside of a length of first triangular core 51 atthree moments of time, correlating to three positions within one quarterof a wave bulge cycle of operation as defined in FIG. 45. Across-section view looking down the longitudinal axis of the firsttriangular core 51 is illustrated in FIGS. 46A-D, showing how thecircular openings 53 in the triangular membranes 52 are offset-from, ordilated away from, and incrementally contract to make contact with, thefifth hollow tube 56 under operation. The corresponding positions withinone quarter of a wave undulation cycle are illustrated in FIG. 47.

When collected water 57 reaches the downstream end of the firsttriangular core 51, it is prevented from traveling further in the samedirection by a flexible cap 58 that closes-off the end of the firsttriangular core 51. (FIG. 43). There is a space between the flexible cap58 and the downstream-end of the fifth hollow tube 56, and the fifthhollow tube 56 is open at its downstream-end. Therefore, captured water57 that has reached the downstream end of the first triangular core 51will enter the downstream-end of the fifth hollow tube 56 and willtravel back along the inside of the fifth hollow tube 56 in a directionopposite to the ambient flowing water 11. Because the fifth hollow tube56 attaches to and enters into the third restraining component 54,collected water 57 will pass into the third restraining component 54 andinto a sixth hollow tube 59 or seventh hollow tube 60 inside the thirdrestraining component 54 after which the water will exit 17 to betransported to a desired destination.

The relatively large volume of flowing water 11 passing over theasymmetric fronds 48 is able to harness kinetic energy which theasymmetric frond unit 49 concentrates onto a relatively small volume ofcollected water 57 within the triangular core 51, creating significantwater pressure within the first triangular core 51, pumping water at arelatively low volume but at a relatively high pressure.

FIG. 48 schematically illustrates another implementation in which thepumping action of the asymmetric frond unit 49 is utilized to generateelectricity by powering a conventional turbine 61. This first generatorimplementation is configured similar to the pump implementation asillustrated in FIG. 43. This first generator implementation however, isnot open at the upstream-end to ambient water, but incorporates aclosed-loop system of circulating water 63, with a turbine introducedinto the loop to harness the kinetic energy of the water 63 movingthrough the closed-loop system.

In this first generator implementation, water 63 of the closed-loopsystem travels along the interior space of the first triangular core 51,and then back along the fifth hollow tube 56, and then into a sixthhollow tube 59, from where it is forced through a turbine 61 whichpowers an electromagnetic generator 62. Upon exiting the turbine 61, thewater 63 passes into at least one eighth hollow tube 64 which feeds intoa second flexible reservoir 65 which adjoins the upstream-end of thetriangular core 51, whereupon the water 63 is passed once again alongthe first triangular core 51 and the process repeats. Apressure-equalization device 66 may be inserted into the closed loopsystem immediately preceding the turbine 61 in order to convert thepulsing nature of the pumping action into a more constant flow. Anotherimplementation utilizes a holding tank up into which water is pumpedafter which it falls via gravity in an even flow, powering a generatoras it flows. In a closed-loop implementation, fluids other than watermay be enclosed and circulated.

The second single-layered-frond pump implementation is similar in designand operation to the first single-layered-frond pump implementation, butwith the addition of an elastic core tube 67 which runs continuouslythrough the circular openings 53 of the elastic triangular membranes 52and which is bonded circumferentially about each circular opening 53 ofeach elastic triangular membrane 52, as shown in the explodedperspective views of FIGS. 49-50. As the triangular membranes 52 expandand contract in diameter under operation, the diameter of the elasticcore tube 67, being bonded to the circular openings 53, also expands andcontracts. When a triangular membrane 52 is at its minimum diameter, theelastic core tube 67 is “pinched” against the fifth hollow tube 56. Whena triangular membrane 52 is at its maximum diameter there is aninterstitial space between the fifth hollow tube 56 and the elastic coretube 67. Under operation, pockets of collected water 57 between thefifth hollow tube 56 and elastic core tube 67 are pushed along insidethe triangular core 51, as illustrated schematically in FIG. 51.

FIG. 52 is a schematic illustration of a second generatorimplementation. This implementation is identical to the first generatorimplementation as illustrated in FIG. 48 with the notable additionalelement of the elastic core tube 67 which is described above andillustrated in FIGS. 49-50.

FIGS. 53A-C illustrate a first triangular core 51 which incorporates aseries of triangular plates 68 which create a triangular valve mechanismfor directing the flow of water pumped through the first triangular core51. In both pumping and generating implementations utilizing thesetriangular plates 68, the fifth hollow tube 56 directing pumped waterback in the direction opposite to the flow of ambient water 11 isabsent. FIG. 56. Pumped water reaching the downstream-end of the firsttriangular core 51 instead enters a third flexible reservoir 69 and atleast one fifth flexible tube 70 that runs across the edge of the end ofat least one ribbon 2 and then enters at least one of the firstrestraining components, where said restraining component is a hollowrigid tube 10 a. Water passes along this rigid hollow tube 10 a whichconnects to and penetrates the third restraining component 54, whereuponthe rigid hollow tube 10 a joins a ninth hollow tube 73 through whichwater passes and exits the mechanism 17 to a desired destination.

FIG. 56 schematically illustrates this third single-layered-frond pumpimplementation, utilizing the triangular plate 68 valve mechanism asdescribed above and in more detail below:

This triangular plate valve mechanism is comprised of triangular plates68, each of which takes the form of an isosceles triangle. FIGS. 54A-Dand FIGS. 55A-D. The two equal edges 71 of each triangular plate 68 arereinforced with a rigid member or material which keeps the lengths ofthese two equal edges 71 constant under operation. The third edge 72 ofthe triangular plate 68 is elastic and fixed to the plane of oneflexible connecting strip 47 in a line that runs perpendicular to thelongitudinal axis of the plane of the flexible strip 47. As describedabove, the cross-sectional dimension of the flexible strip increases anddecreases as the triangle defined by a cross-section through the firsttriangular core 51 expands and contracts under operation. The third edge72 of the triangular plate 68 must therefore become longer or shorterunder operation. Because one end of each of the two equal edges 71 isfixed to either end of the third edge 72, the angle formed by thejuncture of the two equal edges 71 changes under operation, growing moreacute as the third edge 72 shrinks. The angle of the triangular plates68 relative of the flexible strips 47 to which they are attached, andthe fixed lengths of the two equal edges 71 are calibrated so that whenthe first triangular core 51 is at its smallest diameter, the equaledges 71 of three triangular plates 68 meet each other, and thereforeform a closed valve.

FIGS. 54A-D show the configuration of three triangular plates viewedfacing down the longitudinal axis of the first triangular core 51, asthe diameter of the triangular core 51 goes from greatest to smallest,illustrating how the two equal edges 71 of each of the triangular plates68 come together under operation. FIGS. 55A-D show the same sequence butviewed perpendicular to the longitudinal axis of the first triangularcore 51.

FIG. 57 schematically illustrates the third single-layered frondgenerator implementation which is similar in design and operation to thethird single-layered-frond pump implementation illustrated in FIG. 56.In this third generator implementation however, the upstream-end of thetriangular core is not open to ambient water: Instead, water circulatesthrough the mechanism in a closed-loop system, with a turbine introducedinto the loop to harness the kinetic energy of the circulating water ofthe closed-loop system. Enclosed water 63 pumped along the interior ofthe first triangular core 51 exits at the down-stream end into a thirdflexible reservoir 69 from where it is diverted along at least one atleast one fifth flexible tube 70 that runs across the edge of the end ofat least one ribbon 2 and then enters at least one of the firstrestraining components, where said restraining component is a hollowrigid tube 10 a. Water passes along this rigid hollow tube 10 a whichconnects to and penetrates the third restraining component 54, whereuponthe rigid hollow tube 10 a joins a tenth hollow tube 74. The pumpedwater 63 is then pushed through a turbine 61 powering an electromagneticgenerator 62. Water exiting the turbine passes along an eleventh hollowtube 75 which empties into a fourth flexible reservoir 76 which in turnempties into the first triangular core 51 and the cycle is repeatedindefinitely. A pressure-equalization device 66 may be inserted into theclosed loop system immediately preceding the turbine 61 in order toconvert the pulsing pumping action into a more constant flow.

FIG. 58A illustrates a fourth single-layered-frond pump implementation,which is similar in design and operation to the thirdsingle-layered-frond pump implementation illustrated in FIG. 56.However, the fourth single-layered-frond pump implementation differswith the introduction of inner connecting strips 77 which run parallelto the longitudinal axis of the first triangular core 51. The equaledges 71 of the elastic triangular plates 68 are each connected to oneof the inner connecting strips 77. The inner connecting strips 77, beingthemselves connected to each other along their longitudinal lengths,form a tube taking the cross-sectional form of arotationally-symmetrical inverted hexagon. FIG. 58B is a view of thefirst triangular core 51 looking down its longitudinal axis,illustrating how the inner connecting strips 77 form an invertedhexagonal tube affixed to the triangular plates 68.

FIG. 59A illustrates a fourth single-layered frond generatorimplementation, which is similar to the third generator implementationillustrated in FIG. 57, except for the addition in this fourth generatorimplementation of the inner connecting strips 77 and tube as describedabove.

FIG. 59B illustrates a method for assembling and implementingsingle-layered frond mechanisms in one embodiment. A ribbon of flexiblesheet-like material 5901 has forces applied to create one or more planardeformations/undulations in the ribbon 5902. One undulating edge of theribbon is fixed to the undulating edge of a crenated strip 5903. Oneedge of the ribbon is fixed to one edge of the connecting strip 5904,creating an asymmetric frond 5905. Three asymmetric fronds may beadjoined via three connecting strips 5906, creating an asymmetric frondunit 5907. The asymmetric frond unit may be connected to peripheralconnecting structure 5908. The asymmetric frond unit may be anchored ina moving fluid 5909, energy is extracted from, or work is performed by,the asymmetric frond unit 5910.

In another implementation, electrical energy extraction from thedeformed dynamic undulations in the ribbons and other elements of theabove mechanisms which flex in a periodic manner under operation, iswith the utilization of an electroactive material or a material whichexhibits an electrical response to material strain. In suchimplementations of the mechanisms described, two or more electrodes maybe utilized to extract electricity from the electroactive materialutilized in the mechanisms.

Spiral Valve Mechanisms

Implementations of a third category may be characterized as spiral valvemechanisms. Like the first two categories described above, the spiralvalve implementations utilize flexible ribbons 2. However, they do notutilize single-layered fronds 9 or double-layered fronds 9 a asdiscussed above. Like the first two categories, the spiral valvemechanisms are comprised primarily of flexible or elastic components towhich forces are applied during the fabrication so as to deform thesecomponents, after which restraining components, or deformation-retentioncomponents are utilized to maintain these components in their deformed,strained states. The internal energy states of the materials from whichthe components are fabricated are therefore held in strained,non-relaxed states in which they hold the forces applied duringfabrication as potential energy. The potential-energy-holding componentsof the first two categories are primarily the flexible ribbons 2 andcrenated strips 6 and elastic connecting strips 47. Thepotential-energy-holding components of the spiral valve mechanisms areprimarily flexible ribbons 2 and spirals or coils 78, the lattercomprised of a flexible material such as hardened steel, rubber, plasticor any other suitable elastic material with very low plasticity.

For the purpose of clarity, the spiral valve implementation described indetail within the disclosures of this patent utilize three connectedflexible ribbons 2, FIGS. 60A-B. However, spiral valve implementationsutilizing fewer or more connected ribbons are all incorporated into thisinvention. The utilization of three connected flexible ribbons 2 leadsto the use of the world “triangle” when describing components of theimplementation but in implementations utilizing, for example, fourconnected flexible ribbons 2, the word “square” would substitutes theword “triangle” and in an implementation utilizing six connectedflexible ribbons 2, the word “hexagon” would substitute the word“triangle” and so on.

A spiral or coil winds either clockwise or counterclockwise, dependingon viewpoint. An elastic coil may be stretched along its axis by a forceexerted along that axis. An elastic coil may also be made to increase indiameter by securing one end of the coil and twisting it in onedirection and it may be made to decrease in radius by securing the sameend and twisting in the opposite direction, respectively tightening(winding) or loosening (unwinding) the coil.

In the spiral valve implementation, one or more undulating ribbons 2 asdescribed above are secured in multiple locations along a coil 78perpendicular to the circumference of the coil 78. Applying a thirdforce 79 to the connected flexible ribbon 2 perpendicular to the radiusof the coil 78 will cause the coil to tighten or loosen, and thereforeto increase or decrease in radius, at the location of the applied thirdforce 79, so long as the ends of the coil 78 are themselves preventedfrom rotating FIG. 62. In the spiral valve implementation, thesequential and coordinated tightening (winding) of the coil 78, orloosening (unwinding) of the coil directed by the movement ofundulations along the connected flexible ribbons 2 produces pumpingaction as described and explained below.

There are a variety of different methods for the fabrication of thespiral valve in different implementations FIG. 61, whereby potentialenergy is locked into components of the mechanism so that saidcomponents maintain a strained, deformed state prior to operation, andmaintain permutations of this strained, deformed state under operation.In a first such method a first force is applied to a flexible ribbon6101 so as to create a series of undulations in said ribbon 6102 asdescribed above and illustrated previously in FIG. 1. The flexibleribbon 2 is then held in its deformed state 6103 and attached along oneof its longitudinal edges along the length of an elastic coil 78 whilesaid elastic coil 78 with uniform diameter is in a relaxed restingstate, 6104, 6105. Upon removal of the first force 3 the flexible ribbon2 will “want” to return to its straight, un-strained state and in sodoing will exert forces upon the elastic coil 6106, 6107. With correctcalibration of the relative stiffness and elasticity of the ribbon 2 andcoil 78 respectively, some of the potential energy of the stressedflexible ribbon 2 will be transferred into the elastic coil 78. As aconsequence, the flexible ribbon 2 will straighten partially, 6108 andthe elastic coil 78 will become tightened (wound) and loosen (unwound)along its length in a pattern that corresponds to areas of the flexibleribbon 6109 whose wave bulge amplitude falls above or below its neutralaxis. The mechanism is now “charged”, maintaining all of the potentialenergy from the first applied force but in a balanced state, wherebywound and unwound portions of the elastic coil 78 and strains within theflexible 2 ribbon are in balance, 6110. FIG. 63. Illustrates that theelastic coil 78 may be wound or un-wound by applied forces 79.

In the second of at least two methods for the fabrication of the spiralvalve implementations, (FIG. 61) a series of third forces 79 are appliedperpendicular to the radius of the elastic coil 6111 in alternatingrotational directions, causing portions of the coil to rotate partiallyclockwise or counter-clockwise, and therefore causing portions of thecoil to tighten (wind) or loosen (unwind) away from their relaxed state6112. With the coil held in this state 6113 at least one flexible ribbon6114 is attached along one of its longitudinal edges to the coil thecoil 6115. Upon removal of the third force 6116 the coil will “want” toreturn to its pre-strained state and will therefore transfer some of itspotential energy into the attached flexible ribbon 6117, deforming theribbon which will take on an undulating appearance 6119 in a patterncorresponding to regions of the elastic coil that have been wound orunwound 6118 by the application of the third force. With correctcalibration of the relative stiffness and elasticity of the ribbon 2 andcoil 78 respectively, the elastic coil's 78 “desire” to return to auniform diameter is balanced by the flexible ribbon's 2 “desire” to bein its straight and unstrained state. The mechanism is now “charged”with the third force 79 maintained as internal potential energy withinthe mechanism 6120. This internal energy is expressed as a series ofwave undulations within the flexible ribbon 2 corresponding to a seriesof bulges along the elastic coil 78, where said bulges aredemonstrations of regions of the coil 78 that are wound or unwound,which is to say of regions of greater or lesser elastic coil 78diameter.

When such a mechanism is secured within a stream of moving water 11 orother fluid so that the longitudinal axis of the mechanism is parallelto the direction of the stream of water 11, forces acting upon theribbons 2 (FIG. 6) will cause the positions of maximum and minimum wavebulge amplitude to move along the ribbon 2 in the direction of themoving fluid 11. Because the wave undulations in the ribbon 2 correspondwith bulges in the diameter of the elastic coil 78, the bulges in theelastic coil 78 will also move along the mechanism in the direction ofthe moving fluid 11.

A second elastic core tube 80, FIG. 68, is affixed to the inside oroutside of the elastic coil 78 continuously along the length of the coil78 so that the diameter of this second elastic core tube 80 increasesand decreases with the varying diameter of the elastic coil 78. Aneleventh hollow tube 81, FIG. 66, runs continuously within the secondelastic core tube 80 so that pockets are formed between the secondelastic core tube 80 and the eleventh hollow tube 81 when the diameterof the second elastic core tube 80 is greater than its minimum. Wherethe elastic coil 78 and second elastic core tube 80 are at their minimumdiameter, they form a seal against the surface of the eleventh hollowtube 81.

Multiple flexible ribbons 2 may be incorporated, each attached directlyor indirectly along one longitudinal edge to the elastic coil 78. Amultiple of three are chosen and described herein to demonstrate andillustrate a method by which multiply-attached ribbon implementationsare constructed and how they operate.

FIG. 64 illustrates a schematic cross-section through a spiral valvemechanism utilizing three ribbons 2 connected as above and each 120rotational degrees apart. The ribbons 2 are connected to each othercontinuously via second flexible connecting strips 82, which togetherconstitute the second triangular core 83. The second triangular core 83is similar to the first triangular core 51 of the single-layered frondimplementations described above. However, in spiral valveimplementations, the connections between the ribbons 2 and corners ofthe second triangular core 83 are rigid moment connections 83 a. This isdifferent from the attachment of ribbons 2 to the first triangular core51 where the connection is highly flexible or articulated. Therefore.the intersecting angles 84 of the ribbons 2 and second triangular cores83 remain constant under operation in the spiral valve implementationsFIG. 65A-E, whereas the intersecting angle of the ribbons 2 and firsttriangular cores 51 vary under operation in the single-layered frondimplementations as illustrated in FIG. 37A-E.

Another spiral valve mechanism implementation utilizes stiffeningmembers 85 affixed to or incorporated into the material comprising theribbons 2 and second flexible connecting strips 82, FIGS. 69, 70, 71,74. etc. These stiffening members limit the materials ability to bend inone direction, namely in the direction perpendicular to a cross-sectionthrough the material, but do not limit the material's ability to bendperpendicular to a longitudinal-section through the material.

The stiffening members 85 of the ribbons 2 and second flexibleconnecting strips 82 are connected to each other, taking on anarrangement identical to a cross-section cut through the spiral valemechanism as shown in FIG. 64. Internal radial fins or arms 86 connectthe second triangular core 83 to the elastic coil 78 and second elasticcore tube 80. Therefore the forces in the moving water 11 acting on theribbons 2 and on the second triangular core 83 are transferred onto theelastic coil 78 via these internal radial fins or arms 86. The termsinternal radial fins OR arms 86 are used because these components may becontinuous strips multiply connecting the second triangular core 83 andelastic coil 78, or they may be a series of arms multiply connected thesecond triangular core 83 and elastic coil 78.

FIGS. 66, 67, 68, 69,70 illustrate together aspects of the eleventhhollow tube 81, elastic coil 78, second elastic core tube 80, internalradial fins or arms 86, and second triangular core 83 respectively. FIG.71 illustrates these five components assembled together along with theribbons 2. This assembly corresponds to a section of spiral valvemechanism during one cycle of a wave bulge operation.

There are various arrangements and configurations for attaching theinternal radial fins or arms 86 to the elastic coil 78.

One implementation is illustrated in FIGS. 72A-C whereby the internalradial fins or arms 86 are attached to the elastic coil 78 at pointstangent to the circumference of the elastic coil 78. As the secondtriangular core 83 rotates it exerts a force through the internal radialfins or arms 86 which tightens, or winds-up the elastic coil 78,reducing its diameter and closing the space between the second elasticcore tube 80 and the eleventh hollow tube 81, expelling any collectedwater within that space. In this arrangement, the points of attachmentbetween the second triangular core 83 and the internal radial fins orarms 86 are flexible or articulated.

Another implementation is illustrated in FIGS. 73A-C whereby rigidradial arms 87 are secured via rigid connections to the stiffeningmembers 85 of the second triangular core 83. These rigid radial arms 87are inserted into rigid radial tubes 88 which are in turn secured viarigid connections to the elastic coil 78 at points perpendicular to thecircumference of the elastic coil 78. As the second triangular core 83rotates it exerts a force through the rigid radial arms 87 to the rigidradial tubes 88 which tighten, or wind-up the elastic coil 78, reducingits diameter and closing the space between the second elastic core tube80 and the eleventh hollow tube 81, expelling any collected water withinthat space. The rigid radial arms 87 slide within the rigid radial tubes88 under operation. To reduce total friction in the mechanism caused bythe rigid radial arms 87 sliding within the rigid radial tubes 88, FIGS.73A-C show only one rigid radial arm 87 per section of second triangularcore 83 reinforced with stiffening members 85, but any number can beincorporated. In some implementations, there may also be less than onerigid radial 87 arm per wind of the coil 78 so that the rigid radial arm87 attaches to the coil 78 every two or more winds of the coil 78.

FIG. 74 is a wire-frame illustration of a portion of second triangularcore 83 utilizing radial fins or arms 86 to connect the secondtriangular core 83 to the elastic coil 78. For graphic clarity, only oneradial fin or arm 86 is shown connecting to the elastic coil 78 from onecorner of the second triangular core 83, but more may be connected. Insome implementations, there may also be less than one radial 86 arm perwind of the coil 78 so that the radial arm 86 attaches to the coil 78every two or more winds of the coil 78.

FIG. 75 is a wire-frame illustration looking down the center of thelongitudinal axis of a length of second triangular core 83 utilizingradial fins or arms 86 connecting the second triangular core 83 to theelastic coil 78.

FIG. 76 is a wire-frame illustration looking down the center of thelongitudinal axis of a length of second triangular core utilizing rigidradial arms 87.

FIG. 77 is a wire-frame perspective showing a section of a spiral valvemechanism equivalent to one wave bulge undulation, showing thearrangements and relative positions of the components described above,but omitting certain elements for graphic clarity. FIG. 78 is a wireframe elevation of the same portion of spiral valve mechanism viewedperpendicular to the longitudinal axis of the mechanism, showing certainelements of the mechanism. FIG. 79 is the same elevation as FIG. 78 butwith the inclusion of additional elements.

FIG. 80 shows a spiral valve mechanism in the position it assumes whensecured in a stream of water 11. The upstream end of the secondtriangular core 83 has an open flange or collar 89 allowing ambientwater to enter 16. This water is enclosed in a series of pockets thattravel down along the inside of the second elastic core tube 80, underforces exerted upon the ribbons 2 from the stream of water 11, which inturn act upon the elastic coil 78 and second elastic core tube 80 asdescribed above. Water reaching the end of the second elastic core tube80 enters a fifth elastic reservoir 90, after which it is forced back upthe eleventh hollow tube 81 in the direction opposite to the flowingwater 11.

FIG. 81 illustrates how a spiral valve mechanism is secured in a streamof moving water 11 via a third restraining component 54 which is securedto the bed of a river, tidal basin or other stationary object 38. Thethird restraining component 54 may be hinged about its longitudinal axisallowing the spiral coil mechanism to swivel in the moving current so asto maintain a longitudinal axis parallel to the moving current. Thesecond triangular core 83 is fastened via cables 92 or other members tothe third restraining component 54 and the eleventh hollow tube 81 isfastened to the third restraining component 54. Water pumped along theeleventh hollow tube 81 enters the third restraining component 54whereupon it connects to a terminating tube 93 and exiting water 17 isdiverted to a desired destination. FIG. 82 shows a cross-section cutthrough a spiral coil implementation secured in a flowing stream ofwater 17.

FIG. 83 is a schematic illustration of a spiral valve implementationutilized as a pump showing the circulation of pumped water 57 throughthe mechanism.

FIG. 84 is a schematic illustration of a spiral valve implementationutilized as a generator showing the circulation of water. In thegenerator implementation, the pumped water is held within a closed-loopsystem within the mechanism. The pumped water 63 in the eleventh hollow81 tube travels upstream relative to the flowing ambient water 11, theninto a twelfth hollow tube 94, from where it is forced through a turbine61 which powers an electromagnetic generator 62. Upon exiting theturbine 61, the water 63 passes into at least one thirteenth hollow tube95 which feeds into a sixth flexible reservoir 96 which opens into thesecond elastic core tube 80 whereupon the water 63 is pumped in pocketsdown along the space between the second elastic core tube 80 and theeleventh hollow tube 81, into the fifth flexible reservoir 90 and thenback up interior of the eleventh hollow tube 81 and the process repeatsindefinitely. A pressure-equalization device 66 may be inserted into theclosed loop system immediately preceding the turbine 61 in order toconvert the pulsing nature of the pumping action into a more constantflow.

As stated above, more than three or less than three flexible ribbons 2can be utilized in the spiral valve mechanisms. One such implementationis illustrated in FIG. 85 and which utilizes six ribbons 2. Inimplementations utilizing six ribbons 2, the component corresponding tothe second triangular core 83 above will become a first hexagonal core97 comprised of second flexible connecting strips 82 and stiffeningmembers 85.

FIG. 85 also illustrates an arrangement whereby the spiral valvemechanism is harnessed in a conduit or pipe 98 through which a currentof water 11 flows due to a pressure differential between one end of thepipe 98 and the other. The spiral mechanism is secured to this pipe 98via fastening blades 99 across which the current of water flows, actingupon the ribbons 2 and forcing water through the second elastic coretube 80 and back through the eleventh tube 81 where it exits themechanism 17 as described in the implementations above. The kineticenergy in the relatively large volume of water moving through the pipe98 creates significant pressure on the relatively low volume of waterinside the mechanism, creating a low speed, high pressure pump which canalso be utilized to power an electromagnetic turbine in a similar manneras described in the implementations above. The advantage of placing thespiral valve mechanism in a pipe through which water is moving due to apressure gradient is an enhanced interaction between the water currentand the mechanism, as the water has no alternative path to travel otherthan through the array of ribbons 2.

In another implementation, electrical energy extraction from thedeformed dynamic undulations in the ribbons and other elements of theabove mechanisms which flex in a periodic manner under operation, iswith the utilization of electroactive material or material whichexhibits an electrical response to material strain. In suchimplementations of the mechanisms described, two or more electrodes maybe utilized to extract electricity from electroactive elements of themechanisms.

In implementations of the spiral valve mechanisms, the elastic coil 78may be comprised of a helical electroactive material, or incorporateelectroactive material. In such implementations the energy from themoving fluid 11 may be harnessed first by the ribbons 12 as mechanicalenergy and then transferred mechanically to the elastic coil 78 wherethe tightening and loosening of the elastic coil 78 generateselectricity from the electroactive material of the coil 78. Themechanisms described above include facilities for capturing andtransferring forces. For implementations utilizing electroactivematerials, the mechanisms may transfer these captured forces to theelectroactive material.

In yet another implementation, captured fluid may be pumped and/or maypower an electromagnetic generator while at the same time theelectroactive elements of the mechanisms generate electricity.

FIG. 86 is a diagrammatic representation, in one implementation, of theinternal energy state of a single deformation 101 within the flexiblematerial and the internal energy state of a deformation-retainingcomponent 102 which retains the deformation in the material. Thedeformation 101 in the material is in overall compression, and thedeformation-retaining component 102 is in tension.

FIG. 87 is a diagrammatic representation, in one implementation, showingan external force 103 exerted by a moving ambient fluid 104 upon thedeformed flexible material 101. The forces of the moving first fluid 104are transferred 105 to a second fluid 106 as the position of thedeformation moves.

The first fluid 104 of FIG. 87 may, in one implementation, be consideredthe energy-transmitting fluid and may correlate, for example, withelements in these disclosures referred to variously as flowing current11, flowing water 11, flowing stream of water 11 and ambient water 11.

The flexible deformed material 101 of FIG. 87 may, in oneimplementation, be considered the energy-transferring component and maycorrelate, for example, with elements in these disclosures referred tovariously as flexible ribbons 2, crenated strips 6, channels 23,connecting strips 47, triangular core 51, elastic core 67, elastic coretube 80, flexible connecting strips 82 and second triangular core 93.While in some implementations, the first fluid 104 may not make directcontact with this partial list of energy-transferring components, theforces of the first fluid 103 may be transferred 105 directly and/orindirectly to the second fluid 106 by one or more of theseenergy-transferring components.

The second fluid 106 of FIG. 87 may, in one implementation, beconsidered the energy-receiving fluid and may correlate, for example,with elements in these disclosures referred to variously as water inpockets 13, collected water 57, collected ambient water 57, circulatingwater 63, enclosed water 63 and pumped water 63, for example. Theenergy-receiving fluid 106 is transported to a desired location in someimplementations. In other implementations electrical energy may beharnessed from the energy of the energy-receiving fluid 106 by anelectromagnetic generator or other output device, as describedpreviously herein.

Another way to harness electrical energy from components of themechanisms described herein is through the utilization of a flexiblematerial which exhibits an electrical response to a material strain.Such a material would comprise or be incorporated into flexible elementswhich undergo dynamic deformation (e.g., periodically) in the mechanismsdescribed. FIG. 88 illustrates how, in one implementation, two or moreelectrodes 107 may be connected to the deformed flexible material 101,where this material exhibits an electrical response to material straincaused by the forces 103 in the first fluid 104 or forces 105 in secondfluid 106. Examples of such materials include, but are not limited to:electroactive polymers (EAPs) which may exhibit electrostrostrictive,electrostatic, piezoelectric, and/or pyroelectric responses toelectrical or mechanical fields, as well as ionic EAPs, shape memoryalloys, nano-wires, and/or the like.

FIGS. 89-93 diagrammatically illustrate several ways that the energy ofa moving fluid may be harnessed via flexible components of mechanismsdescribed in this invention.

FIG. 89 is a diagrammatic representation, in one implementation, of theinternal energy state of a single deformation 101 within the flexiblematerial and the internal energy state of a deformation-retainingcomponent 102 which retains the deformation in the material. Thedeformation 101 in the material is in overall compression, and thedeformation-retaining component 102 is in tension.

FIG. 90 illustrates one method of energy extraction whereby the force103 in a first fluid acting upon a deformed material 101 causes thedeformation to move and transfer energy via mechanical action 108 to amechanical mechanism to which the deformed material 101 is coupled. Anexample of such a mechanical mechanism may be, but is not limited to, anaxle coupled to an electromagnetic generator or other output device.

FIG. 91 illustrates another method of energy extraction whereby theforce 103 in a first fluid acting upon the deformed material 101 istransferred 105 to a second flowing fluid. The energy of the first fluid103 may be utilized to pump the second fluid, or the energy of thesecond fluid 105 may be used to power an electromagnetic generator.

FIG. 92 illustrates another method of energy extraction whereby theforce 103 in a first fluid acting upon a deformed material 101 causesthe deformation to move thereby creating strains within the deformedmaterial, where said material exhibits an electrical response to amaterial strain. Two or more electrodes 107 may extract electricity fromthe mechanism generated by strains within said material.

FIG. 93 illustrates another possible method of energy extraction wherebythe force 103 in a first fluid acting upon the deformed material 101 istransferred 105 to a second flowing fluid. The energy of the first fluid103 may be utilized to pump the second fluid, or the energy of thesecond fluid 105 may be used to power an electromagnetic generator. Inaddition, the force 103 in the first fluid and second fluid 105 actingupon the deformed material 101 creates strains within the deformedmaterial, where said material exhibits an electrical response to amaterial strain. Two or more electrodes 107 may extract additionalelectricity from the mechanism. In this method of energy extraction,energy is extracted both from strains created in a deformedelectroactive material 101 as described above, as well as from energy105 of the second flowing fluid. Such a dual-energy-harnessing mechanismanticipates novel materials in which elastic deformation does not createheat within the material but instead creates electrical energy, so thatthe energy lost to heat in the arrangement illustrated in FIG. 91 isinstead converted to electrical energy.

It is to be understood that the implementations described hereinfacilitate significant flexibility and that many changes, modifications,variations and other uses and applications of the describedimplementations are possible. All such changes, modifications,variations and other uses and applications which do not depart from thespirit and scope of the invention are deemed to be covered by theimplementations described herein and variants thereof.

What is claimed is:
 1. A fluid transporting apparatus for transporting afirst fluid, comprising: a polygonal tube comprised of flexible wallsenclosing a first fluid passage and having a polygonal cross-section,with a plurality of tube edges corresponding to corners of the polygonalcross-section; a plurality of flexible ribbons, each having a firstlongitudinal edge, a second longitudinal edge, and a contact surface,wherein each of the plurality of flexible ribbons is connected along thefirst longitudinal edge to one of the plurality of tube edges, andwherein the contact surface projects transverse to a longitudinal axisof each of the plurality of flexible ribbons, the longitudinal axisbeing oriented substantially parallel to a primary flow direction of aflowing second fluid, and the contact surface being disposed in contactwith the flowing second fluid; at least one deformation retainingcomponent connected to one of the first longitudinal edge and the secondlongitudinal edge of at least one of the plurality of flexible ribbons;at least one base member fixed with respect to the flowing second fluidand connected to the at least one deformation retaining component; andwherein dynamic undulations of the plurality of flexible ribbons causedby the flowing second fluid impart forces via the flexible walls of thepolygonal tube to a first fluid inside the first fluid passage totransport the first fluid along a longitudinal axis of the first fluidpassage.
 2. The apparatus of claim 1, wherein a volume defined by theflexible walls of the polygonal tube comprises the first fluid passage;the at least one deformation retaining component comprises a pluralityof crenated strips, each having a straight longitudinal edge and anundulating longitudinal edge, wherein each of the plurality of crenatedstrips is connected along the undulating longitudinal edge to the secondlongitudinal edge of one of the plurality of flexible ribbons; and theat least one base member comprises a plurality of base members fixedwith respect to the flowing second fluid and connected to the straightlongitudinal edge of each of the plurality of crenated strips.
 3. Theapparatus of claim 2, wherein the first fluid passage is in operativecommunication with a space containing the flowing second fluid, andwherein the first fluid and the second fluid are the same.
 4. Theapparatus of claim 2, wherein the polygonal cross-section is a triangle.5. The apparatus of claim 2, further comprising: a plurality of flexiblemembranes situated within the polygonal tube and connected to theflexible walls of the polygonal tube, wherein each of the plurality offlexible membranes has an opening, and wherein each of the plurality offlexible membranes and each opening expand and contract in response tothe forces imparted by the dynamic undulations of the plurality offlexible ribbons.
 6. The apparatus of claim 5, further comprising: anelastic core tube bonded to openings of the plurality of flexiblemembranes.
 7. The apparatus of claim 2, further comprising: at least oneinterior tube situated within and substantially concentric with thepolygonal tube.
 8. The apparatus of claim 7, wherein the first fluidpassage is closed to a space containing the second fluid at a closed endin the downstream direction of the flowing second fluid, the at leastone interior tube is at least one hollow interior tube, the at least onehollow interior tube is open to the first fluid passage at an open endof the hollow interior tube in the downstream direction of the flowingsecond fluid, and wherein the first fluid enters the hollow interiortube from the first fluid passage at the open end and is transportedthrough the hollow interior tube in a direction opposite to the primaryflow direction of the flowing second fluid.
 9. The apparatus of claim 2,further comprising: a turbine, disposed in operative communication withthe first fluid passage; and an electromagnetic generator operativelyconnected to the turbine; wherein transport of the first fluid excitesthe turbine to generate electricity via the electromagnetic generator.10. The apparatus of claim 2, further comprising: at least onedirectional valve situated within the polygonal tube and connected tothe flexible walls of the polygonal tube, wherein the directional valvedirects the transport of the first fluid in a preferred direction alongthe first fluid passage.
 11. The apparatus of claim 1, furthercomprising: an elastic core tube enclosed by the polygonal tube anddefining by its internal volume a first fluid passage; wherein the atleast one deformation retaining component comprises an elastic coilconnected by at least two points along its length to the elastic coretube, connected by at least two points along its length to the polygonaltube, and having sequential alternating tightening and loosening toimpart to the elastic core tube a longitudinally variablecross-sectional area; wherein each of the plurality of flexible ribbonshave persistent undulations therein that correlates with the sequentialalternating tightening and loosening of the elastic coil; and whereindynamic undulations of the plurality of flexible ribbons caused by theflowing second fluid impart forces via the elastic coil and elastic coretube to a first fluid inside the first fluid passage within the elasticcore tube to transport the first fluid along a longitudinal axis of thefirst fluid passage.
 12. The apparatus of claim 11, wherein the firstfluid passage is operatively connected to a space occupied by theflowing second fluid, and wherein the first fluid and the second fluidare the same.
 13. The apparatus of claim 11, wherein at least one pointof an inner surface of at least one of the flexible walls of thepolygonal tube is connected to the elastic coil.
 14. The apparatus ofclaim 13, wherein the flexible walls have substantially fixed widths ina direction perpendicular to a longitudinal axis of the polygonal tube.15. The apparatus of claim 14, further comprising: a plurality ofstiffening members affixed to the flexible walls to maintain thesubstantially fixed widths.
 16. The apparatus of claim 13, wherein allof the plurality of flexible ribbons have the same fixed angles withadjacent flexible walls as each other.
 17. The apparatus of claim 13,wherein at least one point of an inner surface of at least one of theflexible walls of the polygonal tube is connected to the elastic coilvia an arm rotatably connected to the at least one point.
 18. Theapparatus of claim 13, wherein an inner side of the flexible walls ofthe polygonal tube is connected to the elastic coil via an arm connectedwith a first fixed angle to the at least one point.
 19. The apparatus ofclaim 11, further comprising: at least one interior tube situated withinand substantially concentric with the elastic core tube.
 20. Theapparatus of claim 19, wherein the elastic core tube is closed to aspace occupied by the flowing second fluid at a closed end downstream ofthe flowing second fluid, the at least one interior tube is at least onehollow interior tube, the at least one hollow interior tube is open tothe first fluid passage at an open end of the hollow interior tubedownstream of the flowing second fluid, and wherein the first fluidenters the hollow interior tube from the first fluid passage at the openend and is transported through the hollow interior tube in a directionopposite to the primary flow direction of the flowing second fluid. 21.The apparatus of claim 11, further comprising: a turbine, disposed inoperative communication with the first fluid passage; and anelectromagnetic generator operatively connected to the turbine; whereintransport of the first fluid excites the turbine to generate electricityvia the electromagnetic generator.
 22. The apparatus of claim 11,wherein the elastic core tube, elastic coil, and the plurality offlexible ribbons are substantially enclosed in a pipe connected to theelastic coil.
 23. The apparatus of claim 11, wherein the elastic coil iscomprised of an electroactive material.
 24. The apparatus of claim 1,wherein at least one of the plurality of flexible ribbons is comprisedof an electroactive material.
 25. The apparatus of claim 1, wherein theat least one deformation retaining component is comprised of anelectroactive material.
 26. A fluid transporting apparatus fortransporting a first fluid, comprising: a first flexible ribbon having afirst longitudinal edge, a second longitudinal edge, and a firstundulating outer contact surface, wherein the first undulating outercontact surface projects transverse to a first longitudinal axis of thefirst flexible ribbon, the first longitudinal axis being orientedsubstantially parallel to a primary flow direction of a flowing secondfluid, and the first undulating outer contact surface being disposed incontact with the flowing second fluid; a second flexible ribbon having athird longitudinal edge, a fourth longitudinal edge, and a secondundulating outer contact surface, wherein the second undulating outercontact surface projects transverse to a second longitudinal axis of thesecond flexible ribbon, the second longitudinal axis being orientedsubstantially parallel to the primary flow direction of the flowingsecond fluid, and the second undulating outer contact surface beingdisposed in contact with the flowing second fluid; a first crenatedstrip having a fifth straight longitudinal edge and a sixth undulatinglongitudinal edge, wherein the sixth undulating longitudinal edge isconnected to the first longitudinal edge of the first flexible ribbon; asecond crenated strip having a seventh straight longitudinal edge and aneighth undulating longitudinal edge, wherein the eighth undulating edgeis connected to the third longitudinal edge of the second flexibleribbon, and wherein the seventh straight longitudinal edge is connectedto the fifth straight longitudinal edge of the first crenated strip; athird crenated strip having a ninth straight longitudinal edge and atenth undulating longitudinal edge, wherein the tenth undulatinglongitudinal edge is connected to the second longitudinal edge of thefirst flexible ribbon; a fourth crenated strip having an eleventhstraight longitudinal edge and a twelfth undulating longitudinal edge,wherein the twelfth undulating edge is connected to the fourthlongitudinal edge of the second flexible ribbon, and wherein theeleventh straight longitudinal edge is connected to the ninth straightlongitudinal edge of the first crenated strip; a base member fixed withrespect to the flowing second fluid and connected to the first crenatedstrip; wherein the first flexible ribbon, the second flexible ribbon,the first crenated strip, the second crenated strip, the third crenatedstrip, and the fourth crenated strip define a first fluid passage, andwherein dynamic undulations of the first flexible ribbon and the secondflexible ribbon caused by action of the flowing second fluid on thefirst undulating outer contact surface and on the second undulatingouter contact surface impart forces to a first fluid in the first fluidpassage to transport the first fluid along a direction substantiallyparallel to the first longitudinal axis of the first flexible ribbon.27. The apparatus of claim 26, wherein the first flexible ribbon and thesecond flexible ribbon have substantially fixed widths in a directionsubstantially perpendicular to the first longitudinal axis and thesecond longitudinal axis.
 28. The apparatus of claim 26, wherein thefirst crenated strip, the second crenated strip, the third crenatedstrip, and the fourth crenated strip have substantially fixed widths ina direction substantially perpendicular to the fifth straightlongitudinal edge, the seventh straight longitudinal edge, the ninthstraight longitudinal edge, and the eleventh straight longitudinal edge.29. The apparatus of claim 26, further comprising: a plurality ofcontinuous elastic extrusions connected to a first undulating innercontact surface of the first flexible ribbon opposite the firstundulating outer contact surface and connected to a second undulatinginner contact surface of the second flexible ribbon opposite the secondundulating outer contact surface, and defining a plurality of channelsoccupied by the first fluid.
 30. The apparatus of claim 29, wherein atleast one of the plurality of channels forms a torqued parallelepiped.31. The apparatus of claim 29, wherein a cross-section of at least oneof the plurality of channels is auxetic.
 32. The apparatus of claim 26,further comprising: at least one flexible tube connected at an end ofthe first flexible ribbon and the second flexible ribbon downstream ofthe flowing second fluid, wherein the first fluid exiting the innervolume enters the at least one flexible tube.
 33. The apparatus of claim32, wherein the at least one flexible tube is connected to the fifthstraight longitudinal edge of the first crenated strip.
 34. Theapparatus of claim 32, wherein the at least one flexible tube isconnected to the first undulating outer contact surface of the firstflexible ribbon.
 35. The apparatus of claim 26, further comprising: aturbine, disposed in operative communication with the first fluidpassage; and an electromagnetic generator operatively connected to theturbine; wherein transport of the first fluid excites the turbine togenerate electricity via the electromagnetic generator.
 36. Theapparatus of claim 26, wherein the base member further comprises: anelongated support member connected to the straight longitudinal edge ofthe first crenated strip, wherein the elongated support member exhibitsat least one of rigidity and tensility.
 37. An apparatus fortransporting fluids, comprising: a first flexible ribbon having a firstlongitudinal edge, a second longitudinal edge, and a first undulatingouter contact surface, wherein the first undulating outer contactsurface projects transverse to a first longitudinal axis of the firstflexible ribbon, the first longitudinal axis being orientedsubstantially parallel to a primary flow direction of a flowing secondfluid, and the first undulating outer contact surface being disposed incontact with the flowing second fluid; a second flexible ribbon having athird longitudinal edge, a fourth longitudinal edge, and a secondundulating outer contact surface, wherein the second undulating outercontact surface projects transverse to a second longitudinal axis of thesecond flexible ribbon, the second longitudinal axis being orientedsubstantially parallel to the primary flow direction of the flowingsecond fluid, and the second undulating outer contact surface beingdisposed in contact with the flowing second fluid; a first flexiblestrip having a first strip edge and a second strip edge, wherein thefirst strip edge is connected to the first longitudinal edge of thefirst flexible ribbon; a second flexible strip having a third strip edgeand a fourth strip edge, wherein the third strip edge is connected tothe third longitudinal edge of the second flexible ribbon, and whereinthe fourth strip edge is connected to the second strip edge of the firstflexible strip; a third flexible strip having a fifth strip edge and asixth strip edge, wherein the third strip edge is connected to thesecond longitudinal edge of the first flexible ribbon; a fourth flexiblestrip having a seventh strip edge and an eighth strip edge, wherein theseventh strip edge is connected to the fourth longitudinal edge of thesecond flexible ribbon, and wherein the eighth strip edge is connectedto the sixth strip edge of the second flexible strip; a first crenatedstrip having a fifth straight longitudinal edge and a sixth undulatinglongitudinal edge, wherein the sixth undulating longitudinal edge isconnected to the second strip edge of the first flexible strip and thefourth strip edge of the second flexible strip; a second crenated striphaving a seventh straight longitudinal edge and an eighth undulatinglongitudinal edge, wherein the eighth undulating edge is connected tothe sixth strip edge of the third flexible strip and the eighth stripedge of the fourth flexible strip; a base member fixed with respect tothe flowing second fluid and connected to the first crenated strip;wherein the first flexible ribbon, the second flexible ribbon, the firstflexible strip, the second flexible strip, the third flexible strip, andthe fourth flexible strip define a first fluid passage, and whereindynamic undulations of the first flexible ribbon and the second flexibleribbon caused by action of the flowing second fluid on the firstundulating outer contact surface and on the second undulating outercontact surface impart forces to a first fluid in the first fluidpassage to transport the first fluid along a direction substantiallyparallel to the first longitudinal axis of the first flexible ribbon.38. A fluid transporting apparatus for transporting a first fluid,comprising: a polygonal tube having flexible walls with adjacent pairsof the flexible walls rotatably connected to each other, wherein thepolygonal tube defines a first fluid passage with an elongate hexagonalcross section and has two wider walls opposite from each other and fourremaining narrower walls than the two wider walls, wherein each of thetwo wider walls have external contact surfaces disposed in contact witha flowing second fluid and formed with persistent spatial undulations ina direction parallel to a longitudinal axis of the polygonal tube, whichis oriented substantially parallel to a primary flow direction of thesecond flowing fluid, the persistent spatial undulations havingsubstantially similar undulatory periods and phases and having aprojection transverse to the longitudinal axis of the polygonal tube; atleast one deformation retaining component connected to the wider wallsto maintain the persistent spatial undulations therein; at least onebase member fixed with respect to the flowing second fluid and connectedto the at least one deformation retaining component; and wherein dynamicundulations of the two wider walls caused by action of the flowingsecond fluid on the external contact surfaces impart forces to a firstfluid in the first fluid passage to transport the first fluid along adirection substantially parallel to the first longitudinal axis of thepolygonal tube.
 39. The apparatus of claim 38, wherein the at least onedeformation retaining component comprises the remaining narrower walls,and wherein each of the remaining narrower walls further comprises: acrenated strip having a straight longitudinal edge connected to anothercrenated strip straight longitudinal edge and an undulating longitudinaledge connected to an undulating longitudinal edge of one of the widerwalls.
 40. The apparatus of claim 38, wherein the at least onedeformation retaining component further comprises: at least two crenatedstrips, each having a straight longitudinal edge connected by at leasttwo points to the at least one base member and having an undulatinglongitudinal edge connected by at least two points to a junction line ofa pair of narrower walls from the four remaining narrower walls.